Details

Time bar (total: 10.6s)

sample40.0ms

Algorithm
intervals
Results
8.0ms36×body2560valid
7.0ms192×body80valid
5.0ms26×body1280valid
3.0ms83×body80nan
2.0ms12×body640valid
1.0ms9×body320valid
1.0ms3×body5120valid
0.0ms2×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0249
1459
2799
3979
41059
51059

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.0b

Counts
2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
139×add-sqr-sqrt
116×*-un-lft-identity
60×times-frac
42×unswap-sqr
36×add-cube-cbrt associate-*l*
30×difference-of-squares
28×distribute-lft-out
24×sqrt-prod
18×associate-*r*
14×distribute-rgt-neg-in
12×associate-/r* *-commutative distribute-lft-out--
10×add-log-exp
9×add-exp-log add-cbrt-cube
6×swap-sqr
5×pow1 associate-/l*
2×cbrt-undiv neg-sub0 associate-+l- flip3-- flip3-+ sqrt-div div-exp sum-log flip-- flip-+ associate-/l/
1×+-commutative sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 diff-log div-sub neg-log prod-exp clear-num cbrt-unprod div-inv
Counts
4 → 178
Calls
4 calls:
41.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
24.0ms
(- (* b b) (* (* 4.0 a) c))
34.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
26.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series326.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
51.0ms
(- (* b b) (* (* 4.0 a) c))
86.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify83.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
06212253
124432157
250032140

prune511.0ms

Filtered
190 candidates to 109 candidates (57.4%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1828190
Fresh000
Picked011
Done000
Total1829191

Merged error: 4.4b

Counts
191 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.2b
(- (* b b) (* (* 4.0 a) c))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
438×times-frac
414×*-un-lft-identity
321×add-sqr-sqrt
188×add-cube-cbrt
100×distribute-lft-out
82×associate-*l*
71×associate-/r*
63×associate-*r*
57×unswap-sqr
50×distribute-rgt-neg-in
30×difference-of-squares
28×associate-/r/
27×*-commutative
25×add-exp-log
24×sqrt-prod
17×associate-/l*
13×add-cbrt-cube
12×div-exp distribute-lft-out--
10×add-log-exp
6×pow1 swap-sqr
5×cbrt-undiv flip3-+ flip-+ div-inv
3×rec-exp 1-exp prod-exp clear-num remove-double-div
2×flip3-- frac-2neg sqrt-div sum-log flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square pow-flip sqrt-pow1 pow1/2 diff-log neg-log cbrt-unprod inv-pow
Counts
4 → 398
Calls
4 calls:
55.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
22.0ms
(- (* b b) (* (* 4.0 a) c))
36.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series358.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(/ 1 (/ (* 2.0 a) (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
49.0ms
(- (* b b) (* (* 4.0 a) c))
83.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify86.0ms

Algorithm
egg-herbie
Counts
410 → 410
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
011755935
150015465

prune493.0ms

Filtered
410 candidates to 170 candidates (41.5%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New4046410
Fresh527
Picked011
Done011
Total40910419

Merged error: 4.3b

Counts
419 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b
(- (* b b) (* (* 4.0 a) c))
0.2b
(* (/ (cbrt 1) (/ a (cbrt 1))) (/ (cbrt 1) (/ 2.0 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
0.5b
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite563.0ms

Algorithm
rewrite-expression-head
Rules
1767×times-frac
1613×*-un-lft-identity
1530×add-sqr-sqrt
1365×associate-/r*
1047×add-cube-cbrt
930×frac-times
808×cbrt-prod
392×associate-/l*
232×distribute-lft-out
166×associate-*l*
141×associate-*r*
134×unswap-sqr
127×add-cbrt-cube
116×distribute-rgt-neg-in
106×associate-/r/
92×cbrt-undiv
77×div-inv
66×clear-num
65×frac-2neg
40×add-exp-log
39×flip3-+ flip-+
35×cbrt-unprod
31×associate-*l/
30×associate-*r/ difference-of-squares
24×sqrt-prod
18×div-exp
12×distribute-lft-out--
10×add-log-exp
9×prod-exp
7×pow1 *-commutative
6×swap-sqr
2×flip3-- sqrt-div sum-log un-div-inv flip--
1×+-commutative neg-sub0 associate-+l- sub-neg rem-sqrt-square sqrt-pow1 pow1/2 diff-log pow-prod-down neg-log
Counts
4 → 1517
Calls
4 calls:
22.0ms
(- (* b b) (* (* 4.0 a) c))
329.0ms
(* (/ (cbrt 1) (/ a (cbrt 1))) (/ (cbrt 1) (/ 2.0 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
35.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
23.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series367.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* b b) (* (* 4.0 a) c))
152.0ms
(* (/ (cbrt 1) (/ a (cbrt 1))) (/ (cbrt 1) (/ 2.0 (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
84.0ms
(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
81.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify352.0ms

Algorithm
egg-herbie
Counts
1529 → 1529
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
0500136377

prune4.6s

Filtered
1529 candidates to 1057 candidates (69.1%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New152901529
Fresh077
Picked011
Done022
Total1529101539

Merged error: 4.3b

Counts
1539 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.9b
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.2b
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
17.3b
(- (pow b 2) (pow b 2))
20.5b
(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
200×*-un-lft-identity
132×add-sqr-sqrt
84×times-frac
59×associate-*l*
52×distribute-lft-out
50×add-cube-cbrt
42×distribute-lft-out--
33×difference-of-squares
26×unswap-sqr
25×sqrt-prod
24×associate-*r*
22×unpow-prod-down
12×associate-/r* unpow2 sqr-pow
11×*-commutative
10×distribute-rgt-out-- add-log-exp
9×add-exp-log add-cbrt-cube
7×associate-/l*
5×pow1
3×flip3-- diff-log swap-sqr flip--
2×cbrt-undiv sub-neg sqrt-div div-exp associate-/l/
1×associate--l- neg-sub0 associate-+l- rem-sqrt-square distribute-rgt-neg-in frac-2neg sqrt-pow1 flip3-+ pow1/2 +-inverses div-sub neg-log prod-exp clear-num cbrt-unprod flip-+ div-inv
Counts
4 → 221
Calls
4 calls:
35.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
55.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
8.0ms
(- (pow b 2) (pow b 2))
25.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

series171.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
1.0ms
(- (pow b 2) (pow b 2))
77.0ms
(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify209.0ms

Algorithm
egg-herbie
Counts
233 → 233
Iterations

Useful iterations: 2 (180.0ms)

IterNodesCost
07292248
141401793
250011786

prune382.0ms

Filtered
233 candidates to 118 candidates (50.6%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2321233
Fresh246
Picked101
Done123
Total2367243

Merged error: 4.3b

Counts
243 → 7

regimes190.0ms

Accuracy

94.9% (1.2b remaining)

Error of 7.0b against oracle of 5.8b and baseline of 29.5b

bsearch215.0ms

Steps
ItersRangePoint
9
2.8787744468916765e+83
8.390568855339406e+90
8.192878813985273e+90
10
-1.627973268244592e-198
-2.2998085647908577e-213
-1.6609875021310342e-211
10
-2.7851241427016145e+159
-9.354797223898085e+144
-6.311729910477647e+146

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04024
14024

end0.0ms

sample1.1s

Algorithm
intervals
Results
243.0ms1031×body2560valid
235.0ms5955×body80valid
165.0ms853×body1280valid
115.0ms2987×body80nan
71.0ms462×body640valid
25.0ms86×body5120valid
25.0ms222×body320valid
10.0ms102×body160valid